An explosion takes place at a certain distance from an army camp. As soon as the sensor in the camp receives the sound of the explosion, a drone starts flying towards the spot of explosion. The drone clicks a picture from the spot and the camp receives it at the same time. Immediately another drone starts flying to the spot and it also sends a picture as soon as it reaches the spot. The two pictures were received at 5:02 PM and 5:05 PM, respectively. If the speed of the drones is 30 m/s, at what time did the explosion take place? Assume that the speed of sound is 300 m/s.

Correct Answer: Option C (4:58:42 PM)

This question tests the concepts of Time, Speed, and Distance (TSD), a core quantitative component of the UPSC Civil Services Aptitude Test (CSAT) Paper-II.

Let the distance from the camp to the explosion be D meters, and let the explosion occur at time T.

1. Second Drone's Journey: The second drone departs exactly at 5:02 PM when the first picture is received. It reaches the spot at 5:05 PM, meaning its travel time is exactly 3 minutes (180 seconds). Using the standard physical formula Distance = Speed × Time, we determine D = 30 m/s × 180 s = 5400 meters.
2. Sound's Journey: The acoustic wave of the explosion travels 5400 meters to the army camp. The time taken by the sound is Time = 5400 m / 300 m/s = 18 seconds.
3. First Drone's Journey: The camp's sensors pick up the sound at T + 18 seconds. The first drone then takes 180 seconds (3 minutes) to travel the 5400 meters, taking and transmitting a picture at 5:02:00 PM. (Because electromagnetic radio waves transmit pictures at the speed of light, this transmission time is practically instantaneous and negligible).
4. Calculating T: Therefore, the timeline is T + 18 seconds + 3 minutes = 5:02:00 PM. Subtracting 3 minutes and 18 seconds from 5:02:00 PM yields the exact time of the explosion: 4:58:42 PM.

Why the other options are incorrect:

• Option A (4:59:00 PM): Incorrect because it subtracts only the drone's 3-minute travel time from 5:02 PM, failing to account for the 18-second acoustic travel time.
• Option B (4:59:02 PM): Incorrect due to an arithmetic error in subtracting the sound travel time.
• Option D (4:56:32 PM): Incorrect as it wrongly subtracts both drones' travel times (6 minutes) from the first picture's timestamp rather than establishing a proper chronological sequence.

Takeaway: In sequential TSD questions involving multiple moving parts, chart the timeline step-by-step. Always isolate the unknown distance by analyzing the most complete time interval (in this case, the second drone's journey).